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Testing in generalized partially linear models: A robust approach

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  • Boente, Graciela
  • Cao, Ricardo
  • González Manteiga, Wenceslao
  • Rodriguez, Daniela
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    Abstract

    In this paper, we introduce a family of robust statistics which allow to decide between a parametric model and a semiparametric one. More precisely, under a generalized partially linear model, i.e., when the observations satisfy yi|(xi,ti)∼F(⋅,μi) with μi=H(η(ti)+xit β) and H a known link function, we want to test H0:η(t)=α+γt against H1:η is a nonlinear smooth function. A general approach which includes robust estimators based on a robustified deviance or a robustified quasi-likelihood is considered. The asymptotic behavior of the test statistic under the null hypothesis is obtained.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 83 (2013)
    Issue (Month): 1 ()
    Pages: 203-212

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    Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:203-212

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    Related research

    Keywords: Generalized partially linear models; Kernel weights; Rate of convergence; Robust testing;

    References

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    1. Wang, Lan & Qu, Annie, 2007. "Robust Tests in Regression Models With Omnibus Alternatives and Bounded Influence," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 347-358, March.
    2. Ana Bianco & Graciela Boente & Elena Martínez, 2006. "Robust Tests in Semiparametric Partly Linear Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 33(3), pages 435-450.
    3. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    4. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
    5. Xuming He, 2002. "Estimation in a semiparametric model for longitudinal data with unspecified dependence structure," Biometrika, Biometrika Trust, vol. 89(3), pages 579-590, August.
    6. Hong-Tu Zhu & Heping Zhang, 2004. "Hypothesis testing in mixture regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 3-16.
    7. Cantoni E. & Ronchetti E., 2001. "Robust Inference for Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1022-1030, September.
    8. Rémillard, Bruno & Scaillet, Olivier, 2009. "Testing for equality between two copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 377-386, March.
    9. Boente, Graciela & Rodriguez, Daniela, 2010. "Robust inference in generalized partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2942-2966, December.
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